Question

Which expression correctly applies the limits to a definite integral?

Options

• \[\int_a^b f(x)\,dx=[F(x)]_a^b=F(b)-F(a)\]

• \[\int_a^b f(x)\,dx=[f(x)]_a^b=f(b)-f(a)\]

• \[\int_a^b f(x)\,dx=F(x)+C\]

• \[\int_a^b f(x)\,dx=[F(x)]_a^b=F(a)-F(b)\]

Answer 1

After finding \(F(x)\), apply the upper limit first and then subtract the value at the lower limit.
Thus \([F(x)]_a^b\) means \(F(b)-F(a)\).